Ruth Milman

Evaluation of a new algorithm for model predictive control based on non-feasible search directions using premature termination

Model predictive control (MPC) is an attractive control methodology because it can deal with constraints directly. Unfortunately however, it is often not possible to implement the strategy, because large MPC horizon times can cause requirements of excessive computational time in solving the quadratic programming (QP) optimization that is necessary at each sampling interval. This motivates the study of developing more effective algorithms for solving QP problems, and of using approximate solutions to the QP problem associated with MPC. In this paper the premature termination of algorithms which solve the QP subproblem are evaluated experimentally using three different algorithms: a proposed new active set method, a conventional existing active set method and a primal-dual interior point method. Results from three representative linearized industrial control system examples are reported on in this paper. Favorable results are found using the proposed new active set method.

Nonlinear Model Predictive Control for Omnidirectional Robot Motion Planning and Tracking With Avoidance of Moving Obstacles

This paper presents a nonlinear model predictive control algorithm for online motion planning and tracking of an omnidirectional autonomous robot. The formalism is based on a Hamiltonian minimization to optimize a control path as evaluated by a cost function. This minimization is constrained by a nonlinear plant model, which confines the solution space to those paths which are physically feasible. The cost function penalizes tracking error, control amplitude, and the presence in a potential field cast by moving obstacles and Boards. An experiment is presented demonstrating the successful navigation of a field of stationary obstacles. Simulations are presented demonstrating that the algorithm enables the robot to react dynamically to moving obstacles.

Real-time analysis for nonlinear model predictive control of autonomous vehicles

This paper presents an online Nonlinear Model Predictive Control (NMPC) framework for trajectory tracking of autonomous vehicles. The operating environment is assumed to be unknown with various different types of obstacles. A bicycle model is used for the prediction of the future states in the NMPC framework, and a fully nonlinear CarSim vehicle model is used for the simulations. Real-time analysis is presented for a particular situation and the effect of warm initialization of optimization process on the computation time is elaborated. Simulation results show that the NMPC controller provides satisfactory online tracking performance while satisfying the real-time constraints, and warm initialization reduces the optimizer computational load significantly.

Obstacle avoidance in real time with Nonlinear Model Predictive Control of autonomous vehicles

A Nonlinear model predictive control (NMPC) for trajectory tracking with the obstacle avoidance of autonomous road vehicles traveling at realistic speeds is presented in this paper, with a focus on the performance of those controllers with respect to the look-ahead horizon of the NMPC. Two different methods of obstacle avoidance are compared and then the NMPC is tested in several simulated but realistic tracking scenarios involving static obstacles on constrained roadways. In order to simplify the vehicle dynamics, a bicycle model is used for the prediction of future vehicle states in the NMPC framework. However, a high-fidelity, nonlinear CarSim vehicle model is used to evaluate the vehicle performance and test the controllers in the simulation results. The CPU time is also analyzed to evaluate these schemes for real-time applications. The results show that the NMPC controller provides satisfactory online tracking performance in a realistic scenario at normal road speeds while still satisfying the real-time constraints. In addition, it is shown that the longer prediction horizons allow for better responses of the controllers, which reduce the deviations while avoiding the obstacles, as compared with shorter horizons.

Guaranteed bounds on the performance cost of a fast real-time suboptimal constrained MPC controller

A fundamental limitation on the implementation of constrained model predictive control (MPC) is the excessive computational time required to evaluate the constrained controls at each sample interval. Prior results show that premature termination of algorithms which solve the quadratic programming (QP) subproblem associated with the computation of the MPC controller at each sampling interval, can be used to decrease the necessary CPU time, with favorable results, but there is no guarantee on the performance of such ad hoc methods. In this paper, a new supervisory algorithm is introduced in order to guarantee bounds on the performance of any non-feasible algorithm, which on solving the QP subproblem is terminated before convergence has occurred. This supervisory algorithm allows for real-time control of a large class of systems using a suboptimal constrained MPC controller with guaranteed bounds on its performance. An example is included to illustrate how this method performs under the limitations of real-time control.

OPTIMAL TRANSIENT RESPONSE SHAPING IN MODEL PREDICTIVE CONTROL

Abstract This paper considers the problem of designing a multivariable model predictive controller (MPC) which results in a time response that is smooth, that has a desired speed of response, and that has small cross-channel interaction. This objective is satisfied, subject to fundamental limitations on achievable performance, by introducing a new cheap-control quadratic performance index that has the desired transient response characteristic embedded within it. Examples are included to show that minimizing the proposed performance index improves the transient response when compared to the standard quadratic performance often used in MPC.

REJECTION OF UNMEASUREABLE EXTENDED CONSTANT DISTURBANCES USING MODEL PREDICTIVE CONTROL

Abstract This paper considers the Model Predictive Control (MPC) set point tracking/regulation problem for a discrete LTI system, which is subject to a class of unbounded disturbances/tracking signals called extended constant signals. The main contribution is a formulation of the systems plant equations under which, for output regulation, no knowledge of the structure or magnitude of disturbances is needed in order to achieve set point regulation for this class of signals. The result is of interest since it implies that no disturbance observer is necessary in order to solve the set point tracking/regulation problem when full-state feedback is available. The results are experimentally verified.

Transient Response Shaping, Model Based Cheap Control, Saturation Indices and MPC

This paper focusses on the time–response performance aspects and control-signal magnitude aspects of controller design. The problem is stated in the context of the servomechanism problem for a class of extended constant tracking/disturbance signals, which includes constant signals as a special case. In particular, the paper proposes a new cheap-control performance index called “model-based cheap control”, which explicitly includes a desired transient model within it; for example, minimizing the performance index with a first-order desired error model results in smooth nonoscillatory transients with almost no cross-channel interaction (subject to standard performance limitations). Assuming the control input signals have a limited operating range, the notion of a “saturation index” (SI) for a closed-loop system is then introduced. The SI gives a measure of the closed-loop operating range that a given controller requires; an SI of one implies that the controller “makes optimal use” of the control signal constraints, while a larger SI implies that the controllers operating range may be highly restricted. The paper then proposes the use of model predictive control (MPC) using the previously introduced model based cheap-control index. In this case, the resulting MPC closed-loop system always has an SI of one, and owing to the special cheap-control performance index used, the system has a transient response that tends to be smooth and non-oscillatory with little cross-channel interaction. Finally, the paper evaluates the performance of a new “non-feasible active set” algorithm to solve the MPC problem; examples are used to show that, in terms of CPU calculation time, the new algorithm can be up to 40 times faster than standard algorithms.

Evaluation of suboptimal real-time control results for model predictive control using improved initial conditions

In the model predictive control (MPC) framework a controller is computed using a finite horizon optimal control cost. When linear constraints are imposed on the system with a quadratic cost function, then the MPC problem can be reformulated as a constrained quadratic programming (QP) problem. In this paper active set methods are used in order to solve the QP problem associated with MPC, and it is shown that it is possible to use information from the previous sample interval in order to provide improved initial conditions for the QP problem which is applied to the subsequent sample interval. Simulations show that when real-time considerations force the used of suboptimal intermediate control values, then improved initial conditions can allow for control values which are closer to the true optimal solution than obtained when using standard initial conditions. These ideas can allow for the implementation of MPC schemes on a greater number of real industrial applications, where standard MPC control cannot be applied due to the excessive CPU time requirements

Design and control of resilient interconnected microgrid for sustained railway

This paper demonstrates the design and control of a resilient interconnected microgrid to support railway infrastructure. A microgrid can alleviate some of the issues due to their proximity to local power substations. When coupled with a transportation network, the microgrid can become useful in supporting the transportation network during regular operation, and emergency events. A grid-connected microgrid will be formed using a photovoltaic system, wind turbine, battery bank and flywheel energy storage system. The microgrid will also be able to take advantage of the recovered energy from the train when it is braking. A microgrid supervisory controller will be used to balance the energy steams exchanged between the train and microgrid. The proposed solution has been demonstrated using simulation and real data, where the achieved results confirm the effectiveness of the proposed control architecture in terms of cost, performance and resilience.